This is a phase I-II dose escalation study of 3'-Azido-2',3'-dideoxyuridine (AzdU), an orally administered nucleoside analog, in adults with HIV infection and helper T lymphocyte counts >300/mm3. This subset of HIV infected persons was selected to not include persons for whom azidothymidine (AZT) has been approved by the FDA. The purpose of the study is to establish a maximal tolerated dose of AzdU and in the process collect data on its potential anti-viral and immune-enhancing effects. The drug will be given for a 12-week period. Blood levels of AzdU will be obtained to establish its bioavailability and single-dose versus multiple- dose pharmacokinetics in humans. The study has been passed by the NIAID- CRS and we are awaiting FDA approval of the IND to begin the study. The importance of this study is that it assesses an antiviral drug for AIDS that may be less toxic but equally effective as AZT.